In publications from colleges/universities, that usually means "graduate class of year". When no institution is specified, it usually means "this institution".
So in this case, it means Divakar (graduate of MIT class of 2001) and Prabhakar (graduate of MIT class of 2004).
To add to your clear response, listing a year without giving any other detail also indicates a Bachelors degree.
If instead they had earned a graduate degree, that would be indicated with some abbreviation for the granting school/college. (I don't know the MIT terms, but at Yale it could be SOM '01, MED '04, LAW '05, etc.)
So in this case, it means Divakar (graduate of MIT class of 2001) and Prabhakar (graduate of MIT class of 2004).